End-point maximal L1 -regularity for the Cauchy problem to a parabolic equation with variable coefficients

Takayoshi Ogawa, Senjo Shimizu

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We consider maximal L1-regularity for the Cauchy problem to a parabolic equation in the Besov space B˙p,10(Rn) with 1 ≤ p≤ ∞. The estimate obtained here is not available by abstract theory of the class of unconditional martingale differences, because the end-point Besov space is included. We consider the end-point estimate and show that the optimality of maximal regularity in L1 for the linear parabolic equation with variable coefficients.

Original languageEnglish
Pages (from-to)661-705
Number of pages45
JournalMathematische Annalen
Volume365
Issue number1-2
DOIs
Publication statusPublished - 2016 Jun 1

Keywords

  • 75C05
  • Primary 35Q05
  • Secondary 35L60

ASJC Scopus subject areas

  • Mathematics(all)

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